Kirchhoff’s loop rule (Kirchhoff’s voltage law) is just energy conservation for a closed circuit loop: the net change in electric potential around any closed path equals zero, so ΣΔV = 0. As you follow a loop, add potential rises (battery EMFs, +ε) and subtract potential drops (IR across resistors, -IR); the algebraic sum must be zero. Use a consistent sign convention: choose a loop direction, mark polarities across sources and resistors, then write ΔV changes as you go. This lets you solve for unknown currents (including cases with internal resistance or multiple loops via mesh analysis). It’s an AP-required tool for free-response and MCQ circuit problems—practice writing loop equations symbolically and checking units. For a short study guide and worked examples see Fiveable’s Topic 11.6 guide (https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN), the full unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-11), and extra practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Because energy is conserved. As a single test charge goes once around any closed loop, it can’t gain or lose net energy—if it did you’d get free energy. Using the CED relation ΔU_E = q ΔV, the net work on charge around the loop is q times the sum of all potential changes. For that product to be zero for any q, the sum of potential differences must be zero: ΣΔV = 0 (Kirchhoff’s loop rule, a direct consequence of conservation of energy). Practically, voltage rises provided by batteries (EMFs) exactly balance voltage drops across resistors and other elements in one complete loop; sign convention just keeps track of rises vs drops when you write the loop equation. This is exactly what AP Topic 11.6 expects you to use on circuit problems (see the Topic 11.6 study guide for worked examples: https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN). For more review, check the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-11) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Kirchhoff’s loop rule is just conservation of energy for electric circuits: if you start at a point and go all the way around any closed loop, the sum of the potential changes equals zero (ΣΔV = 0). That means potential rises (like across a battery, +ε) and potential drops (like across resistors, -IR) must add to zero. Example: going around a simple loop with one battery and one resistor you might write +ε − IR = 0, so ε = IR. Quick how-to: - Pick a direction to traverse the loop (clockwise or CCW). - When you pass from negative to positive terminal of a battery count +ΔV (a rise); the opposite is −ΔV. - When you pass through a resistor in direction of current count −IR (voltage drop); opposite direction is +IR. - Use ΣΔV = 0 to solve for unknowns. Why it matters for AP: it’s in Topic 11.6 (consequence of energy conservation) and shows up in free-response and multiple-choice problems—be ready to combine it with Ohm’s law and internal resistance. For a focused review, check the topic study guide (https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN) and more unit practice (https://library.fiveable.me/ap-physics-2-revised/unit-11).

Kirchhoff’s loop rule (= conservation of energy for a closed circuit) says the algebraic sum of ΔV around any closed loop is zero: ΣΔV = 0. To use it: 1. Pick a loop and choose a direction to traverse (clockwise or counterclockwise). 2. Assign a sign rule: when you go from − to + across a battery that's a potential rise (+ε); across a resistor in direction of current is a drop (−IR), opposite is +IR. Be consistent. 3. Walk the loop adding each ΔV (battery rises, resistor drops) and set the sum = 0. Solve algebraically for unknowns (currents, voltages). 4. If there are multiple loops/branches, write one loop equation per independent loop plus junction (Kirchhoff’s junction rule) equations and solve the system (mesh analysis helps). On the AP exam you must show sign convention and justify ΣΔV = 0 (CED 11.6.A.2). For a quick refresher and worked examples, see the Topic 11.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN) and more unit review (https://library.fiveable.me/ap-physics-2-revised/unit-11). For extra practice problems, check Fiveable’s practice bank (https://library.fiveable.me/practice/ap-physics-2-revised).

Kirchhoff’s loop rule (voltage law) and junction rule (current law) come from two conservation principles and are used in different parts of a circuit. - Junction rule (KCL): conservation of charge. At any node (junction) the sum of currents entering equals the sum leaving: ΣIin = ΣIout (or ΣI = 0 with signs). Use this to relate currents where branches meet. - Loop rule (KVL): conservation of energy. Around any closed loop the algebraic sum of potential differences (including EMFs and drops across resistors or internal resistance) is zero: ΣΔV = 0. Use a consistent sign convention (potential rises for battery + to −, drops across resistors = IR in direction of current) and write loop equations to solve voltages/currents. When solving circuits, first apply junctions at nodes to get current relations, then write loop equations for independent loops to get voltages/currents. The loop rule is explicitly in the CED (11.6.A: ΣΔV = 0). For a focused study and examples, see the Topic 11.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN); for broader review look at the unit page (https://library.fiveable.me/ap-physics-2-revised/unit-11) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Kirchhoff’s loop rule comes straight from energy conservation. Moving a test charge once around a closed circuit returns it to its starting point, so its net change in electric potential energy must be zero. Using ΔU_E = q ΔV (CED 11.6.A.1), that means the sum of the potential changes qΣΔV = 0, so ΣΔV = 0 (CED 11.6.A.2). Practically, that says the total potential rises from batteries (EMFs) exactly equal the total drops across resistors and other elements in any closed loop—no energy mysteriously appears or disappears. On the exam you’ll apply this as ΣΔV = 0 and use sign conventions (potential rise vs drop) to set up loop equations for circuits (Topic 11.6). For a quick review and worked examples, check the AP-aligned study guide (Fiveable) for Kirchhoff’s Loop Rule (https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN) and practice problems for Unit 11 (https://library.fiveable.me/ap-physics-2-revised/unit-11).

You can go either clockwise or counterclockwise—it’s arbitrary. The key is to be consistent with your sign convention as you go around the closed loop and use Kirchhoff’s loop rule (ΣΔV = 0), which follows energy conservation (CED 11.6.A.2). Quick rules that make this easy: - Pick a direction and stick with it for that loop (say clockwise). - When you cross a battery from - to + count a potential rise (+ε); + to - is a drop (−ε). - When you cross a resistor, decide using the resistor’s current: moving in the same direction as the current is a voltage drop (−IR); moving opposite is a rise (+IR). - Write ΔV terms as you encounter elements around the loop, sum them, set equal to zero. If you solve and get a negative current, that just means your assumed direction was opposite. This is exactly what the AP CED expects: apply Kirchhoff’s loop rule and track potential rises/drops (use the study guide for worked examples: https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN). For more circuits practice, check Unit 11 review (https://library.fiveable.me/ap-physics-2-revised/unit-11) and thousands of practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

As you move once around any closed circuit loop, the electric potential returns to its starting value—the net change in potential is zero. That’s Kirchhoff’s loop rule (consequence of energy conservation): ΣΔV = 0. Practically that means you’ll see potential rises across EMF sources (batteries, + to − depending on your path/sign convention) and potential drops across passive elements (resistors, internal resistance) whose magnitudes add up to the rises. You can represent the potentials as V vs. position around the loop: it steps up across a battery and slopes down across resistors and comes back to the original value when you finish the loop. Use consistent sign convention (choose a direction, add + for potential rises, − for drops) when writing loop equations—that’s exactly what AP asks you to do on circuits problems. Review Topic 11.6 on Fiveable (study guide: https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN) and try practice problems in the Unit 11 collection (https://library.fiveable.me/ap-physics-2-revised/unit-11) or the full practice bank (https://library.fiveable.me/practice/ap-physics-2-revised) to get fluent.

Think of voltage (electric potential) like stored energy per charge. When charges move through a resistor, they lose electrical potential energy because collisions with atoms turn that energy into heat. The CED relation ΔU_E = q ΔV shows that a charge q losing energy means ΔV is negative—that’s a voltage drop across the resistor. Kirchhoff’s loop rule (ΣΔV = 0) is just energy conservation: around a closed loop, the rises (like a battery’s EMF) balance the drops (resistors, internal resistance). So a resistor drops voltage because it converts electrical potential energy carried by charges into thermal energy (power P = IΔV or P = I^2R). On the exam, you should be able to state this energy-change view, use ΔU = qΔV, and apply ΣΔV = 0 in loop equations (Topic 11.6 / LO 11.6.A). For a quick refresher, check the Topic 11.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN), the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-11), or practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Start at some point on the loop and pick a direction to follow (your loop sign convention). Plot electric potential V on the vertical axis and position along the loop on the horizontal axis. As you move along an ideal wire (no drop) keep V constant (flat line). When you pass through a resistor in the direction of current, subtract IR—the potential falls (a downward step or a linear slope if you model the resistor as distributed). When you cross a voltage source from negative to positive terminal, add the emf (an upward jump of +ε). Continue around the loop; Kirchhoff’s loop rule requires the net change around the closed path to be zero, so your graph will return to its starting V. Be ready to explain rises vs. drops using ΔU = qΔV and ΔV signs (CED 11.6.A). For AP practice sketching V(x) qualitatively and applying the sign convention, see the Topic 11.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN) and more practice problems at (https://library.fiveable.me/practice/ap-physics-2-revised).

Pick a loop direction first (clockwise or counterclockwise) and stick with it. As you go around the loop add the potential changes ΔV; the algebraic sum must be zero (Kirchhoff’s loop rule, ∑ΔV = 0). Rules you can use every time: - Battery (EMF ε): if you move from the negative terminal to the positive terminal, treat it as a potential rise: +ε. If you go from + to −, it’s a drop: −ε. - Resistor (Ohm’s law): decide the direction of the current I beforehand. If you traverse a resistor in the same direction as the chosen current, that traversal is a potential drop: −IR. If you go opposite the current, it’s a rise: +IR. - Internal consistency: sign comes from change in electric potential (ΔU_E = qΔV). Draw a V vs position sketch if you’re unsure. On the exam, show your loop direction and label each sign—partial credit depends on clear sign convention (CED 11.6.A). For extra practice, check the Kirchhoff’s loop rule study guide (https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN), the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-11), and tons of practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Ohm’s law (V = IR) tells you the voltage–current relation for a single resistor. Kirchhoff’s loop rule (ΣΔV = 0), which comes from conservation of energy (CED 11.6.A.2), is the tool you need when a circuit has more than one element, multiple sources, internal resistance, or loops. Use Ohm’s law to express the drop across each resistor, then use Kirchhoff’s loop rule to sum those drops and the EMFs around a closed path to get equations you can solve for unknown currents or voltages. In short: Ohm’s law gives local element relationships; Kirchhoff’s loop rule ties those elements together in whole circuits (including non-single-resistor cases and multiple batteries). This is exactly what AP asks you to do on circuit FRQs—derive loop equations and apply ΣΔV = 0 (see the Topic 11.6 study guide for worked examples: https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN). For more practice across Unit 11 problems, check the unit page (https://library.fiveable.me/ap-physics-2-revised/unit-11) and the practice bank (https://library.fiveable.me/practice/ap-physics-2-revised).

Energy conservation in circuits means charges don’t gain or lose energy out of nowhere—the work done per charge moving around a closed loop must net to zero. Use ΔUE = qΔV, so a charge q crossing a battery gets a potential rise (qε) and then loses that energy as it goes through resistors (q·IR) as potential drops. Kirchhoff’s loop rule (a consequence of energy conservation) states ΣΔV = 0 for any closed loop: add potential rises and drops with a consistent sign convention and they cancel. Practically: when you go around a loop from the negative terminal, battery = +ε (rise), each resistor = −IR (drop); set ε − ΣIR = 0 to solve currents. You can also sketch V vs position around a loop to show rises at EMFs and linear drops across resistors. This is exactly what AP asks in Topic 11.6 (use ΔUE = qΔV and ΣΔV = 0)—practice these sign conventions and loop equations on the Fiveable study guide (https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN) and more problems at the unit page (https://library.fiveable.me/ap-physics-2-revised/unit-11) or practice bank (https://library.fiveable.me/practice/ap-physics-2-revised).

Equation: ΔU_E = q ΔV. Use it whenever you want the change in electrical potential energy for a charge q moving through a potential difference ΔV (for example, charge through a battery or across a resistor). How it fits with Kirchhoff’s loop rule (Topic 11.6): Kirchhoff’s loop rule is energy conservation around a closed loop: ΣΔV = 0. When you follow a loop, add potential rises (battery/EMF: +ΔV) and potential drops (resistors: −IR, internal resistance: −Ir) so that the algebraic sum is zero. If you need energy instead of voltage, convert with ΔU_E = q ΔV (or use q = IΔt for current flows). When solving problems: pick a loop direction, assign signs for each element consistently, write ΣΔV = 0, substitute ΔV = IR (or EMF − Ir for a real battery), and use ΔU_E = qΔV if the question asks for energy change. For an AP-aligned refresher, see the Topic 11.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN) and unit review (https://library.fiveable.me/ap-physics-2-revised/unit-11). For extra practice, check the Fiveable practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Think of Kirchhoff’s loop rule as energy bookkeeping: around any closed path the net change in electric potential is zero (ΣΔV = 0). Tips to set up loop equations cleanly: - Pick a loop and a direction (clockwise or counterclockwise) and stick with it. - Walk around the loop and add signed ΔV for each element: +ε for a battery when you go from − to + (potential rise), −ε the other way; −IR for a resistor when you go with the current (drop), +IR if you go against the current (rise). - Use consistent sign convention for current direction; if you assumed wrong the algebra gives a negative current. - For circuits with batteries’ internal resistance include ε − Ir terms. - For multi-loop circuits use mesh analysis: write one loop equation per independent loop and use KCL at nodes to relate currents. - Draw a potential vs position sketch if that helps visualize rises/drops (CED: conservation of energy, ΣΔV = 0). Practice a few step-by-step examples until signs feel natural. For guided examples and a focused review see the Topic 11.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-3/6-kirchhoffs-loop-rule/study-guide/uWVN09minOrCqsRN) and more practice problems in Unit 11 or the 1000+ practice sets (https://library.fiveable.me/ap-physics-2-revised/unit-11) and (https://library.fiveable.me/practice/ap-physics-2-revised).